Chapter 9.1, Problem 19E

(a)

To determine

The formula for the local truncation error in $n\text{th}$ step of Euler’s method for initial value problem $y^{\prime }=e^{-y},y\left(0\right)=0$.

(b)

To determine

The bound for local truncation error in each step for the initial value problem $y^{\prime }=e^{-y},y\left(0\right)=0$.

(c)

To determine

The approximate value of $y\left(0.5\right)$ using $h=0.1$ and $h=0.05$ for initial value problem $y^{\prime }=e^{-y},y\left(0\right)=0$.

(d)

To determine

The error in subpart (c) and also the verification of the global truncation error of Euler’s method $O\left(h\right)$.